There N stations on a railroad. After adding X stations on the rail route 46 additional tickets have to be printed. Find N and X

One Answer on this Question

1. Each PAIR of stations means a PAIR of tickets (A to B and B to A)

   2(old stations)(new stations) + 2(new stations)(new stations – 1) = 46

   (N * X) + (X * (X – 1)) = 23

   factoring ___ X (N + X – 1) = 23

   23 is a prime number with only two factors, 1 and 23

   so N = 23 and X = 1

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